Hi Nicholas, 
To search for Births Marriages and Deaths in the UK, first do a search on the following free website www.freebmd.org.uk 

To order certificates you should only use the UK's General Register Office at https://www.gro.gov.uk/gro/content/certificates/login.asp
Once you have registered you can use the search for Births before 1916 which will indicate the mothers family name before marriage,
this website is the only website that I would recommend that you order certificates from.

You will need to search for Boyarsky in the 1911 Census for England & Wales, be aware that when the Government Official recording the
Census wrote down what he thought he heard the name was, you should also search the similar name of"Boyarsk" note no "Y" on the end.

I would suggest that you join the facebook page for the Jewish Genealogical Society of Great Britain.

If you need any advice in UK research you can put messages on the facebook page of the JGS of Great Britain, or contact me!

Best regards,

Michael Hoffman